SOLUTION: Chord AB and CD intersect each other at O inside the circle. AO = 8cm, CO= 12 cm, and DO = 20 cm. If AB is the diameter of the circle, compute the length of arc AC.

Question 1189421: Chord AB and CD intersect each other at O inside the circle. AO = 8cm, CO= 12 cm, and DO = 20 cm. If AB is the diameter of the circle, compute the length of arc AC.
Answer by Edwin McCravy(20060) (Show Source): You can put this solution on YOUR website!


Let P be the center of the circle.  Here are the 
given parts drawn to scale: 



By the intersecting chord theorem,








So radius = half the diameter = 19 cm, AP = 19 = BP



We put those values in the drawing and draw radius CP (in green).
CP is a radius so CP = 19 cm.



We find the central angle APC of arc AC by using the law of 
cosines on ΔCOP, the case is SSS:








 

The formula for the arc length is 
where θ is in radians.  So





Edwin

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